How to enable CUDA rendering without running as root?
Unfortunately I don't have nvidia/cuda on my system, but I happened to notice information that most likely will solve your problem. 
See this link first about information how to install nvidia drivers and enable cuda just to check that you're setup is fine.
And then have a look this forum post where 
Nusaman is using blender with out root (forum post #12). 

To recap:


make sure that you have latest drivers installed. (Nusaman used: cuda-5.5.22-1 and nvidia-334.21-2, but he's using archlinux)
Start blender or some other cuda program (like cudaminer) as root. 
Then close that program (could be that firts render something with blender+cude as root)
Start blender as normal user


What I gathered from multiple sources is that nvidia cuda drivers need to be loaded and for some reason initialison of cuda needs root, but will work with normal user after that.

Please note that you might need extra dkms and dev packages also, to get this working.